To recap: your wife's sex drive is lower than yours, and she logically acknowledges this, but emotionally she can't make the leap to being okay with you having sex with others while still maintaining the sexual relationship you do have?

Does she know why? This is the crux of the matter. And it will determine success or lack thereof.

To me, your wife's feeling that she could tolerate you having an another relationship only after she severs the sexual component of your relationship strikes as a recipe for disaster because it is not coming from a healthy place. In denying you both the sex you do have, she is punishing not only you, but herself. Seems like the perfect breeding ground for resentment.

And while she may not acknowledge it as such, this alternative seems to be saying. "Okay, I will let you have what you want, but it is going to cost you." And you may find that if you act upon it, the cost is higher than you think. Given that she has not provided a healthy solution, you may find that she is terribly hurt by your willingness to pay that price and she is the opposite of okay with it.